How to simplify this fraction?

Can anyone show me how to simplify this fraction:

$$\frac{(k + 1)((k + 1)+1)(2(k + 1)+1)}{6}\;\;.$$

What can be factored out and so forth?

Thanks.

Answer

$$\frac{(k+1)((k+1)+1)(2(k+1)+1)}{6}=\frac{(k+1)(k+2)(2k+3)}{6}$$

Then if $k=2n$ you have

$$\begin{align*} \frac{(k+1)(k+2)(2k+3)}{6}=& \frac{(2n+1)(2n+2)(4n+3)}{6}\\ =&\frac{(2n+1)2(n+1)(4n+3)}{6}\\ =&\frac{(2n+1)(n+1)(4n+3)}{3} \end{align*}$$

it's not so different if $k=2n+1$.
Then if you want you can consider in more detail: what if $n=2m$? And $n=2m+1$?
Enjoy!